共查询到20条相似文献,搜索用时 328 毫秒
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D. Suryanarayana 《Aequationes Mathematicae》1978,18(1-2):322-329
In this paper, we discuss the pairs (f, h) of arithmetical functions satisfying the functional equation in the title, whereF is the product off andh under the Dirichlet convolution; that is,F(n) = Σ d|n ?(d)h(n/d) andS(m n) = Σd|(m, n) ?(d)h(n/d). The well-known Hölder's identity is a special case of this functional equation (?(n) =n, h(n) = μ(n)). We also generalize the functional equation in the title to any arbitrary regular arithmetical convolution and discuss the pairs of solutions (f, h) of the generalized functional equation and pose some problems relating to the characterization of all pairs of solutions. 相似文献
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H. Brass 《Aequationes Mathematicae》1975,13(1-2):151-154
Remark on the estimation ofE n [x n+2m ]. Let be $$E_n [f]: = \mathop {\inf }\limits_{p \in P_n } \mathop {\sup }\limits_{x \in [ - 1, 1]} |f(x) - p(x)|$$ (P n : set of all polynomials of degreen). Riess-Johnson [4] proved (3) $$E_n [x^{n + 2m} ] = \frac{{n^{m - 1} }}{{2^{n + 2m - 1} (m - 1)!}}[1 + O(n^{ - 1} )],n even.$$ This degree of approximation is realized by expansion in Chebyshev polynomials and by interpolation at Chebyshev nodes. The purpose of this paper is to give a more precise estimation by constructing the polynomial of best approximation on a finite set. This construction is easily done and one obtains the result, that the termO(n ?1) in (3) may be replaced by 1/2(m ? 1) (3m + 2)n ?1 + O(n ?2). 相似文献
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Kondagunta Sundaresan 《Israel Journal of Mathematics》1965,3(3):139-146
A characterisation of uniformly non-1
n
/(1)
Orlicz space is obtained intrinsically in terms of the Young function determining the Orlicz space. It is shown that a uniformally
non-1
n
/(1)
Orlicz space is reflexive.
This work was supported in part by Air Force Grant G2A-152015. 相似文献
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K. Navickis 《Lithuanian Mathematical Journal》1988,28(2):162-174
V. Kapsukas Vilnius State University. Translated from Litovskii Matematicheskii Sbornik (Lietuvos Matematikos Rinkinys), Vol. 28, No. 2, pp. 299–314, April–June, 1988. 相似文献
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It is shown that every super-simple (m, n) ring is equationally complete. The atomic varieties of (m, 2) rings and the atomic varieties of (2,n) rings are completely determined. 相似文献
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《Journal of the Egyptian Mathematical Society》2014,22(2):167-173
In this paper, we introduce the concept of fundamental relation θ1 on an (m, n)-hypermodule M as the smallest equivalence relation such that M/θ1 is a commutative (m, n)-module, and then some related properties are investigated. 相似文献
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We investigate the class of generalized convex sets on Grassmann manifolds, which includes known generalizations of convex sets for Euclidean spaces. We extend duality theorems (of polarity type) to a broad class of subsets of the Euclidean space. We establish that the invariance of a mapping on generalized convex sets is equivalent to its affinity. 相似文献
20.
Characterizations of ( m,n )-Jordan Derivations and ( m,n )-Jordan Derivable Mappings on Some Algebras
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Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n = 0. An additive mapping δ from R into M is called an(m, n)-Jordan derivation if(m +n)δ(A~2) = 2 mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every(m, n)-Jordan derivation with m = n from a C*-algebra into its Banach bimodule is zero. An additive mappingδ from R into M is called a(m, n)-Jordan derivable mapping at W in R if(m + n)δ(AB + BA) =2mδ(A)B + 2 mδ(B)A + 2 nAδ(B) + 2 nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left(right) separating set generated algebraically by all idempotents in A, then every(m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital(A, B)-bimodule and U = [A M N B] is a generalized matrix algebra, then every(m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. 相似文献